Frequency selective circuits



Jan. 5 1926.

H. W. ELSAS'SER FREQUENCY sELEC'rIv'E: CIRCUITS Filed August 13, 1920 15 Sheets-Sheet 1 Cmmmwh CSQ@ gs@ v Jal; 5, 192s. 1,568,142

H. w. -ELsASsER FREQUENCY SELECTIVE CIRCUITS I.

Filed August l5, 1920 l 3 Sheets-Sheet 2 fBf/swser ATTORNEY 5 INVENTORv Jan. 5 1926. l1,568,142

H. W. ELSASSER FREQUENCY SELECTIVE CIRCUITS INVENTOR ATTORNEY Patented Jan. 5, 1926.

UNITEo STATES PATENT OFFICE.

HENRY W. ELSAS'SER, OF NEW YORK. N. Y ASSIGNOR T0 AMERICAN TELEPHONE AND TELEGRAPH COMPANY, A CORPORATION OF NEW YORK.

FREQUENCY SELECTIVE CIRCUITS.

Application led August 13, 1920. Serial No. 403,368.

To all whom it may concern:

Be it known that I, HENRY `W. ELsAssER, a citizen of the United States, residing at New York, in the county of New York and State' 6 of New York, have invented certain Improvements in FrequencyvSelective Circuits, of which the following is a specification.

This invention relates to frequency-selective circuits.

It contemplates a network of impedances having a period of series resonane and a Vperiod of parallel resonance, so that its impedance for a certain frequency of current is very low and for another, very high.

Theinvention proposes, further, the use of a network-of this character in combination with other impedance elements in a g periodic structure of the type illustrated and described in the patents to G. A. Campbell, 1,227,113 and 1,227,114 of May 22, 1917. Certain new and useful types of wave filters are thus arrived at, the characteristics of whi'h are explained hereinbelow.

This application is related to certain copending cases, Serial Numbers 403,367, 403,369, 403,370, led of even date herewith.

A good understanding of the invention may now be had from tHe following description of certain specific embodiments thereof, having reference to the accompanying drawing, in which,

ig.`1 is a dia rammatic view showing one form of networ embodying the invention; Figs. 2 to 5 inclusive are dia rammaticy views showing various types of lters comprising the networkl of Fig. l;

Fig. 1^ is a graph showing the variation with fre uency in the impedance of the netf work of ig. 1, and

Figs. 2^ to 5A inclusive, are graphs show ing the variation in attenuation of they filters of Figs. 2 to 5, respectively'.

Similar characters'of reference designate similar yparts in each of the several views.

The network of Fig.- 1 consists of an inductance Ll in series with a. pair of parallel paths, one. of which contains an inductance 2 and the other of which comprises a condenser C2. The impedance of the inductance Ll 1s jwLl, where j is written for the 1/-1 and w equals 21rf,f being the frequency of the current. The impedance of Place for convenience f1=r 2) where f, is the frequency at which L2 and Cz are in resonance with each other. Sub-l stitute equation (2) in equation (l) and simplify. Then above equation may be placed equal to Kp Then ' Z: jwrLzK (4) where The variation in the value of K with frequency is shown by the curves in Fig. 1A, in which the values of K are ordinates and the ratios off to f, are abscissae. These curves indicate also the manner in which the mpedance of the network changes with frequency, as may be seen by an inspection of equation 4. At low frequencies, the impedance of the network is a small, positive value, which iinreases as the frequency is.

raised until-at the point of resonance of L2 and C2, the value thereof 1s infinite. In`

frequency. It is thus seen that the network of l has two periods of resonance, a

perio of parallel resonance at one frequency and a period of series resonance at a higher frequency. The point of parallel resonance is dependent upon the relative values of only two of the impedance elements, namely L, and C2, and the point of series resonance is governed by the relative proportions of all three of the impedance elements. The curves of Fig. 1A are drawn for an ideal network containing no resistance or other dissipative element, but in any actual case, the resistance may be made so small that its effect is practically negli ible. It thus appears that the network of ig. 1 may be used as a selective network-for passing current of series resonant frequency and preventing the passage of current of parallel resonant frequency.

I have found, moreover, that by employing the network asa shunt and series 1mpedance in a periodic structure like that discussed in the. Campbell patents herembefore mentioned, certain new types' of wave filters are arrived at, which filters have certain new and valuable characteristics which I shall now describe.

Figs. 2, 3, 4 and 5 illustrate four types of filters, employing the network of Fig. 1, the first two of these views showing the network as a shunt impedance element and the last two as the series impedance element of the filter section. Figs. 2 and 3 show an inductive and a capacity reactance respectively as the series impedance element, and Figs. 4-and 5 show the same reactances, respectively, as the shunt impedance element.

The properties of the'above filters may be determlned from certain mathematical expressions which set forth the relations existing between the frequency of current and the impedance elements of the filters. In the Campbell patents hereinbefore mentioned, it was shown (equation 2) that for a periodic structure of the type now under consideration, in which the series impedance per section is Z1 and the shunt impedance per section is Z2, the attenuation per section of the filter may be derived from the relation cosh 2 Z nation 6, when the corresponding values o Z,L and Z2 are substituted therein. For the filter shown in Fig. 2, the value of Z1 is 7) n and (according to equation 4 above),

Z2=jwrL2K (8) The resultant equation for cosh l/ is, therefore 1 jwLo cosh '-ZjwrLzK-l-l (9) Fig. 2^ is a graph showing the Variation of the attenuation of the filter of Fig. 2, as computed from equation 9. The axis of the abscissae is laid of in ratios of f to f, and the axis of the ordinates in values of the attenuation constant per lter section. An inspection of the curves shows that the attenuation isnil for a range of frequencies extending between f1 and fh. At a frequency fm in the upper attenuated range, the attenuation is infinite and when this fre- 'quency is chosen close to fh, as shown in Fig. 2^, the filter has'a sharp cut-off for frequencles ly1ng just above fh.

The frequencies fl, fh and fm may be evaluated as follows: It was shown in the said Campbell patents that for unattenuated transmission must be a pure imaginary, and that, therefore, the value of cosh must lie between i1. The frequencies which limit the ranges of freey transmission may consequently be determined by placing equat1on`9 e ual to +1 and -1 respectively and solving or f. When this is done, it will be found that the roots are respectively,

.fh :2" Lzczalo +4111) (11) The frequency fm, at which the attenuation is infinite, may be evaluated by lacing equation 9 equal to and solving or f, whence i i 1 L1+L2 m= 12 vf 211' LILZCZ purpose of both.- It has, moreover, a freiquency fm at which the attenuation is innite. This frequency may be chosen close to f, thus giving the filter a sharp cut-off for frequencies just below the high-pass ran e.

e frequencies fo, f2, f3, and fm maybe evaluated similarly as the limiting frequencies of the filter of Fig. 2. The expression for cosh in the present case is, since C, 1s a capac1ty reactance,

l @aufn-1mm 13) wrLzK n Placing equationV 13 equal respectively to +1 and -1, and solving for f, the roots will be found to be solved for f, the frequency of maximum atcosh 2 jwLo (18) p which is similar to equation 9 above, excep that the values of Z,L and Z2 are interchan ed, the shunt impedance of Fig. 2 being t e series impedance of Fig. 4, and vice versa. Thev limiting frequencies are 0btained, as before, by placing cosh equal to +1 and -1 respectively, and solving for f. Then lThe expression for the frequency of maximum attenuation, fm, is obtained by placin cosh 1 equal to 'and solving for Then The curves of Fig. 54 show that the filter of Fig. 5 is of the double band type and similar to that of Fig. 3, differing therefrom, however, in that one of the ranges of free transmission extends from 0 to f2, thus making the filter a combined low-pass and band filter. The frequency fm of infinite attenuation lies close to the frequency f2, thus 'ving this filter a sharp cut-off for the ow 4pass range.

The attenuation curve of Fig. 5A is derived from the expression wx-LZK and the .values of fo, f2, f3, f4 and fm are obtained b Vplacing the above expression for cosh y equal to 1, 1 andrespectively.

Thus

eozo

It should be noted that the attenuation curves illustrated herein refer to the ideal structure in which the resistance of the impedance units is zero. In a practical filter there is a departure from these curves, owmg to energy dissipation. In any case, however, the resistance may be made so small that the departure from the ideal is practically negligible.

The formulae 10-12, 14-17, 19-21, and 23-26, given above, may be used 1n designing filters to meet any specified sets of conditions. Since there are four independent impedance elements in each filter section, any four properties of the filter dependent upon the values of the impedance elements but independent of each other may be chosen at will. For example, in the desi of a filter of the type illustrated in Fig. 3, two of the design conditions may be taken as the frequencies fo and f2, and a third as f3, thus defining the ranges of free transmission. This leaves one condition open to choice, and this may be `taken as the impedance of the filter at any desired frequency, or as the value of any one of the elements of the filter section. In the design of a filter of the type of Fig. 2, two

formulae, let it be required to design a filter of the type illustrated in Fig. 5, which shall transmit all frequencies between 5,000 and 20,000 cycles, and which shall pass also all frequencies below 3,000 cycles. Frequencies fwa and f4 are thus specified as 3,000, 5,000 an 20,000 cycles respectively. As a fourth design factor, let it be assumed that certain considerations dictate that the value of Co shall be .025 microfarads. This leaves three constants of the filter section,l namely L1, L2 and C2 to be determined. It will be noted that formulae 23, 24, and 25 are three simultaneous equations involving the three unknown constants. When, therefore, the values of f2, f3, f, and C0, assumed`abpve, are substituted in these equations, they may solved for the three unknowns. When this is done it will be found that L1=.0106 henries. L2=.0176 henries. (12:.154 microfarads.

. stood that the above example is merely a simple illustration, and in no way limits the invention.

Although only certain forms of filters embodying the invention are shown and described herein, it is readily understood that various changes and modifications may be made therein within the scope of the following claims, without departing fronti the spirit and scope of the invention.

What is claimed is:

1. In a wave filter of the type having like recurrent sections, each section consisting of a series element and a shunt element, a complete element consisting of a network of impedances'so arranged and so proportioned that at low frequencies the reactance thereof has a small positive value which increases as the frequency is raised to a large positive value, then undergoes a sudden change from a large positive to a large negative value, and thereafter decreases in negative value, finally becoming increasingly positive.

2. In a wave filter ofthe type having like recurrent sections, each section consisting of a series element and a shunt element, a complete element consisting of a network comprising an inductive reactance in series with a pair of parallel paths, one of which comprises a capacity reactance and the other of which comprises an inductive reactance.

3. A filter for an electric circuit consisting of a plurality of sections, each section consisting of an impedance `in series with the circuit and an impedance in shunt thereto, said impedances being determined as functions of certain definite parameters so that the filter transmits without substantial attenuation all frequencies lying above a limiting frequency and such frequencies as lie 1n a band below said limiting frequency, the limits of said band being neither zero nor said limiting frequency, while attenuating and approximately suppressing currents of neighboring frequencies lying outside the above-defined limits, the attenuation being approximately a maximum at a frequency lying between said limiting frequency and the upper limit of the said band, said parameters being said limiting frequency and the upper and lower limits of said band and the mid-section characteristic Vimpedance of the filter at an extreme frequency.

4. A filter for an electric circuit, consisting of a plurality of sections, each section comprising an impedance inseries with the circuit and animpedance in shunt thereto, one of said impedances consisting of a single reactance element and the other of a network comprising an inductive reactance in series with a pair of parallel paths, one of which comprises acapacity reactance and the other an inductive reactance.

1,ees,142

5. The method of discriminating lamong alternating current components according to their frequency which consists` in attenuatcurrents from -zero frequency to n. cerl tain finite frequency, then assing currents from that frequency -to anot er higher finite frequency, then attenuating currents from the last mentioned frequency u to a third finite frequency still higher, an then pessing all currents of higher frequency than lo said third finite frequency and developing n. maximum of attenuation at a frequency a little less than said third finite frequency.

In testimony whereof, I have signed my name to this specification this 10th day of ll .August 1920.

HENRY W. ELsAssER. 

